I chose Anderson in my first game, but TBH I think Udina is the better choice.
Anderson is a nicer guy, there's no doubt about that. But you can't say that Udina isn't acting in humanity's best interest. The fact that he has the personality of a turd isn't relevant. He's a politician who has loads of experience with promoting humanity's interests with the Council, while Anderson is an old warhorse without a shred of experience when it comes to intergalactic politics.
When it comes to choosing between the asshole who I can trust to do a decent job or the nice guy who'll spend the rest of his days whining about how politics aren't his thing, the choice isn't hard to make.
It's kinda like the choice at the end of ME2: You have the good guy option (choosing Anderson / destroying the base) that the game obviously expects you to take, and the other option (choosing Udina / giving the base to Cerberus) that the game goes out of its way to tell you it's a bad choice, but that makes more sense.
I mean, you've got this enemy from beyond the stars that you know nothing about except that they're extremely evil, unimaginably powerful, and currently heading your way. You've also got the single greatest source of information of that enemy in your hands. Then, the game expects you to destroy the one thing that could help you understand the Reapers. Yeah yeah I know, Reaper indoctrination this and Cerberus abuse that, blah blah blah. But when it comes to saving the galaxy I'd willingly choose the evil I know over the all-powerful space gods coming this way to feast on my delicious bio-mass. No matter how much every fucking person on my ship questions that decision.